Image-guided systems designed for neurosurgery, hip surgery, spine surgery and other anatomy that is relatively rigid can use rigid body transformations to accomplish image registration. These systems often rely on point-based registration to determine the transformation, and many such systems use fiducial markers, attached to rigid anatomical features, to establish accurate fiducial points for the registration. Image-guided radiotherapy and radiosurgery systems, for example, may use intra-operative x-ray imaging systems to generate images that can be registered with synthetic x-ray images (digitally reconstructed radiographs, or DRRs) derived from 3-dimensional pre-operative scan data (e.g., computed tomography or magnetic resonance imaging) that is used for treatment planning. Such systems may achieve sub-millimeter accuracy in fiducial registration, but also require that the patient be exposed to x-rays periodically during treatment (e.g., every 5 seconds).
In situations where the patient's total x-ray exposure needs to be limited, or where an invasive surgical procedure requires the presence of a surgeon and operating room personnel, the use of intra-operative x-ray imaging may be severely limited or prohibited. In such situations, x-ray imaging may be replaced or supplemented with an optical or magnetic tracking system. The tracking system is used to track the locations of fiducial markers that are attached to the patient (e.g., directly attached or integrated into a rigid frame that is attached to the patient). If the tracking system is calibrated to the intra-operative imaging system, then locations of the fiducial markers can then be registered with the intra-operative imaging data to insure that the treatment or procedure conforms to the treatment plan.
The tracked locations of the fiducial markers on the patient are used to find a rigid transformation between the coordinate space of the patient on the operating table and the corresponding space in the pre-operative images of the patient, which visualize the same fiducial markers at known locations. The known locations of the fiducial markers may be used to calculate the rotations and translations that best map the coordinate space of the patient to the pre-operative image space. The information can be used to position the patient in the operating room or to position a robotically controlled surgical instrument relative to the patient to conform treatment to a treatment plan based on the pre-operative scan data.
Such tracking systems, however, are subject to measurement error. One component of error is random error, often called noise or jitter. The effects of random error may be reduced by taking many measurements at a given location and averaging the results because random error has an average value of zero. Another component of error is position-dependent bias, which varies over space but remains constant at any given point. Position-dependent bias may be caused, for example, by miscalibrations of lenses in an optical tracking system or local magnetic field distortions in a magnetic tracking system.